First, CH does not postulate that wave function is ontological. Second, CH is not deterministic.

Thanks for being the only one out of over 100 people reading this topic to answer:)

According to what I've read Hawking believe in a "Consistent Histories" Everettian type interpretation.
Where only a few worlds become "real", while hte rest are just possibilities.
Then you got the CH of Gellman and Hartle, this too seems to say the wavefunction is ontological.

What you argue is that if you want ontological wavefunction without collapse you have to accept either DeWitt/Deutsch type MWI or Bohm?

Thanks for being the only one out of over 100 people reading this topic to answer:)

According to what I've read Hawking believe in a "Consistent Histories" Everettian type interpretation.
Where only a few worlds become "real", while hte rest are just possibilities.
Then you got the CH of Gellman and Hartle, this too seems to say the wavefunction is ontological.

What you argue is that if you want ontological wavefunction without collapse you have to accept either DeWitt/Deutsch type MWI or Bohm?

There aren't many people here who know the consistent histories approach. I don't know it well enough myself to give a good answer to those questions. (I've been thinking that I should read this more carefully for a couple of years now, but it has never reached the top of my "to do" list since I first skimmed it). Regarding your last point, I think that what you would have to accept if you decide to view the state vector as ontological, in the version of QM that's based on the most popular set of axioms, is a different type of MWI. One that doesn't throw out the Born rule, like Everett did, and that relies on decoherence to tell us which worlds are "interesting" in the sense that they can contain conscious observers.

Isn't CH just the ontological interpretation that's based on a slightly different set of axioms for QM? (It's been too long since I skimmed that article, so I don't even remember what it's based on. Unfortunately I don't have time to read about it or get deeply involved in a discussion about it now). I like to think of a "theory" as defined by its axioms rather than by its predictions, and if CH is based on different axioms, it's a different theory in my book (but probably equivalent to standard QM in the sense that it makes the same predictions). So maybe CH and the MWI I'm talking about should be thought of as very similar interpretations of two different but equivalent theories.

But again, I hardly remember anything about the CH, so don't take what I said about it too seriously. I'm serious about the MWI though.

What you argue is that if you want ontological wavefunction without collapse you have to accept either DeWitt/Deutsch type MWI or Bohm?

Yes.

Concerning CH, I would say it is a variant of the Copenhagen interpretation (CI), in the sense that QM only says what are the probabilities of different measurement outcomes. However, the difference is the following. If you perform many measurements at different times on the same system, CH treats it as a single measurement - the measurement of the whole history of the system. For that reason you do not need the collapse of the wave function in CH. CH says what is the probability of a given history.